Lecture 13 - Radiosity I

foraa a face we have top face have for fortopface

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Unformatted text preview: cos ⇡ r2 j |A| These deltadelta form factors can be computed and stored up •  These form factors can be computed and stored in a look in table. look up table. ! a •  They can then be applied to every patch without the Theyeed for further formto everycalculations. ! the need for n can then be applied factor patch without further form factor calculations. Graphics Lecture 13: Slide 28! . 24 / 29 Computing delta form factors Computing the the form factors Computing the delta form factors Computing the delta form form Computing the deltadelta factors factors " Computing Graphics Lecture 13: Slide 29! ! Foraa a face we have: top face have: For Fortopface wewe have: For For toptopface we have: ! a top a face wehave: ! 1 1 11 cos i cos = i cos = = = jcos j j= ! cos cosi icoscos= jr= =r r r ! | soso so the factorfactor4 isA||4 | the the form factor| is!|AA form form is ⇡Ais | | the soso form factor is ⇡⇡r r4 the form factor r r4 ⇡ ! ! For a side face we have: Foraaside face wehave: For a a sideface wehave: side face have: For Forsideface we wehave: ! zp 1 ! cos i = cos j = z 1 r =1 1 cos r = zzp p p cos = cos j cos i !cos i i= r cos jj = = r rr zp |A| rr ! so the form factor is ⇡r4 z| |A| p so form factor so the form factorisiszp|rA| sothe theformfactoris is p!⇡A4r4 the form factor z 4 | so ⇡r⇡ ! ! . 25 / 29 ! Problem Break Problem Break Problem Break " Given that thehemi-cube is defined at the origin,origin, the -axis Given that thethe hemi-cube is defined atorigin,with the zz -axis Given that hemi-cube is defined at the the with with the vertical what is the delta the factor for the following two vertical what is the delta form delta form thefollowing two z-axis vertical what is form factor for factor for the following hemi-cube pixels inthe top the zz=face, hemi-cube pixels inpixels inface, top=11: z = 1: ! : two hemi-cube the top face, {{xmin , ymin , xmax , ymax }= {{ 0005, , 0005, , 005, , 005}} xmin , ymin , xmax...
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